A computed tomograph comprises, inter alia, an X-ray tube, X-ray detectors arranged in the form of rows or a matrix and which represent individual detector channels, and a table on which the patient is supported. The X-ray tube and the X-ray detectors are arranged on a gantry which rotates around the table on which the patient is supported, or around an examination axis running parallel to it, during the measurement. As an alternative to this, the X-ray detectors may also be arranged on a fixed detector ring around the table on which the patient is supported, with the X-ray tube being moved with the gantry.
The table on which the patient is supported can generally be moved relative to the gantry along the examination axis. The X-ray tube produces a focused beam which widens in the form of a fan in a slice plane at right angles to the examination axis. The boundary of this focused beam in the direction of the slice thickness is set by means of the size or the diameter of the focus on the target material of the X-ray tube and one or more shutters which are arranged in the beam path of the focused X-ray beam. During examinations in the slice plane, the focused X-ray beam passes through a slice of an object, for example a body slice of a patient who is supported on the table on which the patient is supported, and strikes the X-ray detectors which are opposite the X-ray tube. The angle at which the focused X-ray beam passes through the body slice of the patient and, if appropriate, the position of the table on which the patient is supported vary relative to the gantry continuously while images are being recorded by the computed tomograph.
The intensity of the X-rays in the focused X-ray beam which strike the X-ray detectors after passing through the patient is dependent on the attenuation of the X-rays as they pass through the patient. In this case, each of the X-ray detectors produces a voltage signal as a function of the intensity of the received X-ray radiation, which voltage signal corresponds to a measurement of the global transparency of the body for X-rays from the X-ray tube to the corresponding X-ray detector or detector channel. A set of voltage signals from the X-ray detectors, which correspond to attenuation data from which attenuation values are calculated, and which have been recorded for a specific position of the X-ray source relative to the patient is referred to as a projection. A set of projections which have been recorded at different positions of the gantry during rotation of the gantry around the patient is referred to as a scan. The computed tomograph records a large number of projections with the X-ray source in different positions relative to the body of the patient, in order to reconstruct an image which corresponds to a two-dimensional section image through the body of the patient, onto a three-dimensional image. The normal method for reconstruction of a section image from recorded attenuation data or from attenuation values derived from such data is referred to as the filtered back-projection method.
The reconstruction process is based on the fact that it is possible to calculate correct attenuation values for each detector channel k and for each projection angle of the gantry or each projection p. However, in practice, the detectors are never perfect. In fact, in addition to other faults, they have individual spectral nonlinearities, which may differ from channel to channel. Thus, the attenuation values             x      k        ⁡          (      d      )        =      -          ln      ⁡              (                                            I              k                        ⁡                          (              d              )                                            I            ok                          )            which are calculated from the signal from the individual detector elements or detector channels is a function of the thickness d of the material through which the radiation has passed, and which also depends on the respective detector channel k. Ik(d) represents the remaining signal of the X-ray radiation as measured by the detector channel k after passing through the material or the body, and Iok represents the corresponding unattenuated signal. The dependency xk(d) measured using X-ray detectors is admittedly nonlinear in any case owing to the hardening of the beam as it passes through the material, but this nonlinearity can be taken into account jointly in the data evaluation by means of an appropriate beam hardening correction, jointly for all the channels. The remaining errors must be detected in a separate correction process. A correction process such as this, in particular for the described spectral nonlinearities, is necessary in order to avoid image artifacts in the form of rings in the images recorded with the computed tomograph.
In this case, it is known for these channel-specific spectral errors to be approximated by use of a polynomial, which is specific to each detector channel k, in the form:       Δ    ⁢                   ⁢          x      k      ccr        =            ∑              n        =        1            N        ⁢                   ⁢                  a                  k          ,          n                    ·              x        k        n            where the degree of polynomial N is generally not greater than 2. The data measured with each detector element or detector channel is in this case converted to logarithmic form in the known manner described above, in order to obtain an attenuation value xk. This attenuation value is finally corrected by use of the correction value Δxkccr which is determined specifically for each channel, before the filtered back-projection process is carried out using the attenuation values.
The major technical problem with this type of correction is to determine the polynomial coefficients ak,n, which are also referred to as channel correction coefficients in the following text. At the moment, measurements are carried out on bar phantoms of different thickness, without the gantry being rotated, in order to determine the polynomial coefficients using the computed tomograph. These measurements result in two or more different attenuation values for each detector channel. From these, if the attenuation of the respectively used phantoms is known, it is possible to determine a discrepancy from the correct value, and thus the correction coefficients. However, measurement by using these bar phantoms is tedious. Furthermore, the bar phantoms are relatively bulky and must be delivered with each computed tomography system and must be stored at the point where they are used. The measurement must also be carried out on a non-rotating system, so that the system state when determining the correction coefficients does not correspond to the state in which it is used for an actual measurement. In particular, the temperature conditions when the system is in the stationary state may differ considerably from the temperature conditions in the rotating state.
A further type of fault which is caused by the detector elements in the computed tomograph is so-called spacing errors, which are caused by the detector layout not being geometrically equidistant. To a first approximation, these spacing errors can be approximated by the following formula:       Δ    ⁢                   ⁢          x      k      sp        =            c      k        ·                            ∂                      x            k                                    ∂          k                    .      
In addition, the spacing coefficients ck must be determined in order to use this correction for the attenuation values xk which are derived from the measurements. These spacing coefficients ck have until now been determined by a scan of a cylindrical phantom made of plexiglass with a relatively small diameter of only 40 mm, which is positioned eccentrically within the examination area of the computed tomograph. The sinogram which is obtained in this way is first of all used to determine the position of the phantom within the computed tomograph. This position is then compared with the data obtained for each detector channel, and the correction coefficient is derived from the distance between the respective maxima. Both the positioning of the phantom and the data evaluation are, however, relatively complex.